The Paretian liberal with intuitionistic fuzzy preferences: A result

In the present paper we consider a situation in which the individual preferences and the social preference relation are intuitionistic fuzzy and study the compatibility between the Pareto principle and Sens minimal liberalism condition. A possible factorization of the intuitionistic fuzzy weak preference relation allows us to prove a possibility result for the case of max-min transitive social preference.I am extremely grateful to the Coordinating Editor and an anonymous referee of this journal for their detailed comments and suggestions. The paper was written while I was a Post-doc fellow at the Graduiertenkolleg Allocationstheorie, Wirtschaftspolitik und kollektive Entscheidungen, Ruhr-University Bochum. Thanks are due to Krassimir Atanassov, Luis G. Gonzalez-Morales and Gergana Dimitrova for helpful comments, and to the Deutsche Forschungsgemeinschaft for financial support.     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

On Myopic Stability Concepts for Hedonic Games

We present a unified look at myopic stability concepts for hedonic games, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and present a sufficient condition for the existence of contractually Nash stable coalition structures on the class of separable games. We gratefully acknowledge financial support from the Alexander von Humboldt Foundation (D. Dimitrov)“by “D. Dimitrov gratefully acknowledges financial support from the Alexander von Humboldt Foundation.     

Status-seeking in hedonic games with heterogeneous players

We study group formation by heterogeneous players when players’ preferences are dictated by status-seeking. Status can be intrinsic or associative. Considering these two types of status as either complements or substitutes results in non-emptiness of the core of the corresponding games and allows for a full characterization of the core stable outcomes.     

The complexity of shelflisting

Theory and Decision - Optimal shelflisting invites profit maximization to become sensitive to the ways in which purchasing decisions are order-dependent. We study the computational complexity of...     

Simple Priorities and Core Stability in Hedonic Games

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. We characterize internally stable coalitions on the proposed domains and show how these characterizations can be used for generating a strict core element in the first case and a core element in the second case. Moreover, we prove that an element of the strict core under friends appreciation can be found in polynomial time, while finding an element of the core under enemies aversion is NP-hard.